Selected Rheological Properties of Some Tomato Ketchups
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Lecture 1: Introduction
Lecture 1: Introduction E. J. Hinch Non-Newtonian fluids occur commonly in our world. These fluids, such as toothpaste, saliva, oils, mud and lava, exhibit a number of behaviors that are different from Newtonian fluids and have a number of additional material properties. In general, these differences arise because the fluid has a microstructure that influences the flow. In section 2, we will present a collection of some of the interesting phenomena arising from flow nonlinearities, the inhibition of stretching, elastic effects and normal stresses. In section 3 we will discuss a variety of devices for measuring material properties, a process known as rheometry. 1 Fluid Mechanical Preliminaries The equations of motion for an incompressible fluid of unit density are (for details and derivation see any text on fluid mechanics, e.g. [1]) @u + (u · r) u = r · S + F (1) @t r · u = 0 (2) where u is the velocity, S is the total stress tensor and F are the body forces. It is customary to divide the total stress into an isotropic part and a deviatoric part as in S = −pI + σ (3) where tr σ = 0. These equations are closed only if we can relate the deviatoric stress to the velocity field (the pressure field satisfies the incompressibility condition). It is common to look for local models where the stress depends only on the local gradients of the flow: σ = σ (E) where E is the rate of strain tensor 1 E = ru + ruT ; (4) 2 the symmetric part of the the velocity gradient tensor. The trace-free requirement on σ and the physical requirement of symmetry σ = σT means that there are only 5 independent components of the deviatoric stress: 3 shear stresses (the off-diagonal elements) and 2 normal stress differences (the diagonal elements constrained to sum to 0). -
Information to Users
INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrougb, substandard margins, and improper alignment can adversely afreet reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. • Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. A Bell & Howell Information Company 300 North Z e e b Road. Ann Arbor. Ml 48106-1346 USA 313/761-4700 800/521-0600 ANALYSIS OF MORPHOLOGY, CRYSTALLIZATION KINETICS, AND PROPERTIES OF HEAT AFFECTED ZONE IN HOT PLATE WELDING OF POLYPROPYLENE DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree of Philosophy in the Graduate School of The Ohio State University By Jenn-Yeu Nieh, B.S., M.S. -
A Basic Introduction to Rheology
WHITEPAPER A Basic Introduction to Rheology RHEOLOGY AND Introduction VISCOSITY Rheometry refers to the experimental technique used to determine the rheological properties of materials; rheology being defined as the study of the flow and deformation of matter which describes the interrelation between force, deformation and time. The term rheology originates from the Greek words ‘rheo’ translating as ‘flow’ and ‘logia’ meaning ‘the study of’, although as from the definition above, rheology is as much about the deformation of solid-like materials as it is about the flow of liquid-like materials and in particular deals with the behavior of complex viscoelastic materials that show properties of both solids and liquids in response to force, deformation and time. There are a number of rheometric tests that can be performed on a rheometer to determine flow properties and viscoelastic properties of a material and it is often useful to deal with them separately. Hence for the first part of this introduction the focus will be on flow and viscosity and the tests that can be used to measure and describe the flow behavior of both simple and complex fluids. In the second part deformation and viscoelasticity will be discussed. Viscosity There are two basic types of flow, these being shear flow and extensional flow. In shear flow fluid components shear past one another while in extensional flow fluid component flowing away or towards from one other. The most common flow behavior and one that is most easily measured on a rotational rheometer or viscometer is shear flow and this viscosity introduction will focus on this behavior and how to measure it. -
A Constitutive Framework for the Non-Newtonian Pressure Tensor of a Simple fluid Under Planar flows
A constitutive framework for the non-Newtonian pressure tensor of a simple fluid under planar flows Remco Hartkamp∗ and Stefan Ludingy Multi Scale Mechanics, Faculty of Engineering Technology, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands B. D. Toddz Mathematics Discipline, Faculty of Engineering and Industrial Sciences and Centre for Molecular Simulation, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia (Dated: May 24, 2013) Non-equilibrium molecular dynamics simulations of an atomic fluid under shear flow, pla- nar elongational flow and a combination of shear and elongational flow are unified consis- tently with a tensorial model over a wide range of strain rates. A model is presented that predicts the pressure tensor for a non-Newtonian bulk fluid under a homogeneous planar flow field. The model provides a quantitative description of the strain-thinning viscosity, pressure dilatancy, deviatoric viscoelastic lagging and out-of-flow-plane pressure anisotropy. The non-equilibrium pressure tensor is completely described through these four quantities and can be calculated as a function of the equilibrium material constants and the velocity gradient. This constitutive framework in terms of invariants of the pressure tensor departs from the conventional description that deals with an orientation-dependent description of shear stresses and normal stresses. The present model makes it possible to predict the full pressure tensor for a simple fluid under various types of flow without having to produce these flow types explicitly in a simulation or experiment. I. INTRODUCTION There is significant scientific and industrial interest in describing the relation between the pres- sure tensor for non-Newtonian fluids out of thermodynamic equilibrium and other quantities, such as the strain rate and the fluid density and temperature. -
Rheology Theory and Applications
5KHRORJ\ 7KHRU\DQG$SSOLFDWLRQV TAINSTRUMENTS.COM &RXUVH2XWOLQH Basics in Rheology Theory Oscillation TA Rheometers Linear Viscoelasticity Instrumentation Setting up Oscillation Tests Choosing a Geometry Transient Testing Calibrations Applications of Rheology Flow Tests Polymers Viscosity Structured Fluids Setting up Flow Tests Advanced Accessories TAINSTRUMENTS.COM %DVLFVLQ5KHRORJ\7KHRU\ TAINSTRUMENTS.COM 5KHRORJ\$Q,QWURGXFWLRQ Rheology: The study of stress-deformation relationships TAINSTRUMENTS.COM 5KHRORJ\$Q,QWURGXFWLRQ Rheology is the science of flow and deformation of matter The word ‘Rheology’ was coined in the 1920s by Professor E C Bingham at Lafayette College in Indiana Flow is a special case of deformation The relationship between stress and deformation is a property of the material ୗ୲୰ୣୱୱ ౪౨౩౩ ୗ୦ୣୟ୰୰ୟ୲ୣ ൌ ౪౨ ൌ TAINSTRUMENTS.COM 6LPSOH6WHDG\6KHDU)ORZ Top plate Area = A x(t) Velocity = V0 Force = F y y Bottom Plate Velocity = 0 x F Shear Stress, Pascals σ = A x(t) σ γ = η = Shear Strain, % Viscosity, Pa⋅s y γ γ -1 γ = Shear Rate, sec t TAINSTRUMENTS.COM 7RUVLRQ)ORZLQ3DUDOOHO3ODWHV Ω r θ h Stress (σ) ߪൌ మ ൈM ഏೝయ r = plate radius h = distance between plates γ ߛൌೝ ൈθ M = torque (μN.m) Strain ( ) θ = Angular motor deflection (radians) Ω= Motor angular velocity (rad/s) ೝ Ω Strain rate (ߛሶ) ߛሶ ൌ ൈ TAINSTRUMENTS.COM 7$,QVWUXPHQWV5KHRPHWHUV TAINSTRUMENTS.COM 5RWDWLRQDO5KHRPHWHUVDW7$ ARES G2 DHR Controlled Strain Controlled Stress Dual Head Single Head SMT CMT TAINSTRUMENTS.COM 5RWDWLRQDO5KHRPHWHU'HVLJQV Dual head or SMT Single head or CMT Separate motor & transducer Combined motor & transducer Displacement Measured Transducer Sensor Torque (Stress) Measured Strain or Rotation Non-Contact Drag Cup Motor Applied Torque Sample (Stress) Applied Strain or Direct Drive ^ƚĂƚŝĐWůĂƚĞStatic Plate Rotation Motor Note: With computer feedback, DHR and AR can work in controlled strain/shear rate, and ARES can work in controlled stress. -
Antisymmetric Stress Tensor
SOFT DISSIPATIVE MODES IN NEMATODYNAMICS Arkady I. Leonova1 , Valery S. Volkovb a) Department of Polymer Engineering, The University of Akron, Akron, Ohio 44325-0301, USA. b) Laboratory of Rheology, Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Pr., 29, Moscow 117912 Russia. Abstract The paper analyses a possible occurrence of soft and semi-soft dissipative modes in uniaxially anisotropic nematic liquids as described by the five parametric Leslie-Ericksen-Parodi (LEP) constitutive equations (CE’s). As in the similar elastic case, the soft dissipative modes theoretically cause no resistance to flow, nullifying the corresponding components of viscous part of stress tensor, and do not contribute in the dissipation. Similarly to the theories of nematic elastic solids, this effect is caused by a marginal thermodynamic stability. The analysis is trivialized in a specific rotating orthogonal coordinate system whose one axis is directed along the director. We demonstrate that depending on closeness of material parameters to the marginal stability conditions, LEP CE’s describe the entire variety of soft, semi-soft and harder behaviours of nematic viscous liquids. When the only shearing dissipative modes are soft, the viscous part of stress tensor is symmetric, and LEP CE for stress, scaled with isotropic viscosity is reduced to a one-parametric, stress - strain rate anisotropic relation. When additionally the elongation dissipative mode is also soft, this scaled relation has no additional parameters and shows that the dissipation is always less than that in isotropic phase. Simple shearing and simple elongation flows illustrate these effects. Keywords: Director; Nematics; Internal rotations; Dissipation; Soft deformations. 1. -
On the Effect of Different Material Constitutive Equations in Modeling Friction Stir Welding: a Review and Comparative Study on Aluminum 6061
International Journal of Advances in Engineering & Technology, Mar. 2014. ©IJAET ISSN: 22311963 ON THE EFFECT OF DIFFERENT MATERIAL CONSTITUTIVE EQUATIONS IN MODELING FRICTION STIR WELDING: A REVIEW AND COMPARATIVE STUDY ON ALUMINUM 6061 M. Nourani, A. S. Milani*, S. Yannacopoulos School of Engineering, University of British Columbia, Kelowna, Canada ABSTRACT In the present article, first a review of various thermomechanical approaches applied to modeling of friction stir welding (FSW) processes is presented and underlying constitutive equations employed by different researchers are discussed within each group of models. This includes Computational Solid Mechanics (CSM)-based, Computational Fluid Dynamics (CFD)-based and Multiphysics (CSM-CFD) models. Next, by employing an integrated multiphysics simulation model, recently developed by the authors for FSW of aluminum 6061, the effect of some common constitutive equations such as power law, Carreau and Perzyna is studied on the prediction of process outputs such as temperature, shear rate, shear strain rate, viscosity and torque under identical welding conditions. In doing so, unknown parameters of the power law dynamic viscosity model were identified for the aluminum 6061 near solidus by fitting the related equation to Perzyna dynamic viscosity model response with the Zener-Hollomon flow stress. Effects of Zener-Hollomon and Johnson-Cook flow stress models are also analyzed in the same example by predicting the shear stress around the FSW tool. Based on the conducted comparative study, some agreeable results and consistencies among outcomes of specific constitutive equations were found, however some clear inconsistencies were also noticed, indicating that constitutive models should be carefully chosen, identified, and employed in FSW simulations based on characteristics of each given process and material. -
A Narrow-Gap Rotational Rheometer for High Shear Rates and Biorheological Studies
A narrow-gap rotational rheometer for high shear rates and biorheological studies Ein Dünnspaltrotationsrheometer für hohe Scherraten und biorheologische Untersuchungen Der Technischen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg zur Erlangung des Doktorgrades Dr.-Ing. vorgelegt von Haider Mohammed Ali Dakhil, M.Sc. aus Bagdad-Irak Als Dissertation genehmigt von der Technischen Fakultät der Universität Erlangen-Nürnberg Tag der mündlichen Prüfung: 12.02.2016 Vorsitzender des Promotionsorgans: Prof. Dr.-Ing. habil. Peter Greil Gutachter: Prof. Dr.rer.nat. Andreas Wierschem Prof. Dr.rer.nat. Rainer Buchhloz Acknowledgement I am very grateful to Prof. Dr. rer. nat. Andreas Wierschem for his supervision and astute insight during the course of my Ph.D degree at the Institute of Fluid Mechanics (Lehrstuhl für Strömungsmechanik, LSTM). My sincere gratitude also goes to Prof. Dr.-Ing. habil. Antonio Delgado who gave me the opportunity to be a part of this project and has been a constant support throughout. I would like to acknowledge the Iraqi Ministry of Higher Education and Scientific Research (MoHESR) and the German Academic Exchange Service (Deutscher Akademischer Austauschdienst, DAAD) for their financial support during my stay in Germany. My appreciation and gratitude to my present and former colleagues in the research group (High Pressure Thermofluiddynamics and Rheology Research), M.Sc.Monika Kostrzewa, and M.Sc. José Alberto Rodriguez Agudo. At this juncture, I would express my special thanks to Dr.-Ing. Holger Hübner and Mrs. Anette Amtmann for their valuable advice and support. This work would have been more difficult without their cooperation. I owe a lot to the technical assistance provided by Mr. -
Rheology – the Purely Viscous (Generalized Newtonian) Fluid
Rheology – The Purely Viscous (Generalized Newtonian) Fluid All materials deform if a high enough force, or stress (force/area), is applied. The normal response to a stress is a change in momentum. If we think of a 3-D flow, we realize that when a small element of fluid enters a volume element, it may, in addition to experiencing the same force, experience a new force causing a change in direction of its momentum. In other words, momentum in the z-direction can become momentum in the x- direction. A simple example is fluid above a moving plate, impinging on a second plate. It is flowing in shear (x-direction) until it hits the plate. The primary stress is the shear stress exerted by its confining wall or walls (see Fig. 1, Rheo1). The second plate exerts a new force on the fluid, causing a change in momentum perpendicular in direction to the moving plate. It seems like a simple process to analyze. For almost all polymeric fluids, this process would be impossible to analyze analytically, and would even be very difficult to describe numerically, even given the fastest possible computer. Three reasons: (1) The equations relating stress to strain or strain rate for polymer fluids are not known exactly. (2) The change in direction of momentum leads to PDEs which are highly nonlinear. (3) The flow at the plate may be turbulent (3-D), and it is hard to describe 3- D turbulence even in simple Newtonian fluids such as water. Therefore we usually try to describe polymer flows in a way in which it does not become necessary to account for changes in momentum. -
New Rheology Models, Non-Newtonian Formulations and Multiphase Flows
New rheology models, non-Newtonian formulations and multiphase flows GEORGIOS FOURTAKAS THE UNIVERSITY OF MANCHESTER [email protected] 5th Dualsphysics Users Workshop 1 5 t h – 17th March 2021 Outline • Motivation • Mathematical description of non-Newtonian flows • Implementation • Input configuration (xml file) • Examples • Work in progress • Conclusions 5th Dualsphysics Users Workshop 2 1 5 t h – 17th March 2021 Motivation • Not all fluids are Newtonian • Industrial applications use fluids that exhibit non-Newtonian characteristics • These are usually multi-phase flows of complex fluids Corn starch at 30Hz • Two or more phases with: • different densities • different viscosities (at rest) • varying viscosity under stress • exhibit a yield strength Credit: www.youtube.com by bendhoward 5th Dualsphysics Users Workshop 3 1 5 t h – 17th March 2021 Description of non-Newtonian flows • A non-Newtonian fluid viscosity is depended on shear stress/rate/history • Usually, non-Newtonian fluids do not exhibit linear shear stress-rate behaviour • In DualSPHysics v5.0 we have implemented time independent fluids • A number of combinations and options are possible Bingham- pseudoplastic Bingham pseudoplastic Newtonian Viscoelastic Bingham- behaviour dilatant Shear stress Shear Time dependant non- Newtonian pseudoplastic Dilatant behaviour Yield strength Fluid Time independent Newtonian dilatant behaviour Bingham type Shear rate 5th Dualsphysics Users Workshop 4 1 5 t h – 17th March 2021 Mathematical description of non-Newtonian flows -
Determination of Apparent Viscosity As Functionof Shear Rate And
ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 4, Issue 5, November 2014 Determination of Apparent Viscosity as Function of Shear Rate and Fibres Fraction in Polypropylene Lukáš Likavčan, Miroslav Košík, Jozef Bílik,Maroš Martinkovič, Where vx is velocity in the x direction. The relations between Abstract—apparent viscosity of short fibre-reinforced plastics viscosity ( ), shear stress ( ), and shear rate ( ) is: depends on the shear rate (because it is Non-Newtonian Fluid), (3) melt temperature, fibre fraction etc.Therefore, it is very important to know their basic mathematical model. This paper presents examples of measuring apparent viscosity of the same polypropylene with different filler fraction (glass fibres in this case). From the viscosity of unfilled material and 10% filled material, we can calculate viscosity for other filled materials. This mathematical formula is discussed in this paper. Index Terms—plastics, polypropylene, fillers, glass fibres, rheology, apparent viscosity. I. INTRODUCTION Fig. 1 A volume unit of liquid moving at shear rate under the Recently, fibre-reinforced thermoplastic composites have applied shear stress of found wide application in structural and non-structural A Newtonian fluid is the one in which viscosity is applications because of their excellent mechanical properties. independent of the shear rate. In other words, a plot of shear Structural parts a prepared by injection moulding, where stress versus shear strain rate is linear with slope . In moulds are manufactured by machining – milling and Newtonian fluids, all the energy goes into the molecules grinding. For this application currently new polymer sliding by each other. -
Rheology and Rheometry
Rheology and Rheometry Paula Moldenaers Department of Chemical Engineering Katholieke Universiteit Leuven W. De Croylaan 46, B-3001 Leuven Tel. 32(0)16 322675 Fax 32(0)16 322991 http://www.cit.kuleuven.ac.be/cit. ρειν = flow Rheology = The Science of Deformation and Flow Why do we need it? - measure fluid properties - understand structure-flow property relations - modelling flow behaviour - simulate flow behaviour of melts under processing conditions Processing conditions shear rate [s-1] Sedimentation 10-6 –10-4 Leveling 10-3 Extrusion 100-102 Chewing 101 -102 Mixing 101-103 Spraying, brushing 103 -104 Rubbing 104 -105 Injection molding 102 -105 coating flows 105 -106 How about Newtonian behaviour? 1. Constant viscosity 2. No time effects 3. No normal stresses in shear flow 4. η(ext)/η(shear) = 3 Symbols: ε° ⇒ D σ⇒T s ⇒σ Newton’s law: T = -pI +η 2D Contents 1. Rheological phenomena 2. Constitutive equations 2.1. Generalized Newtonian fluids 2.2. Linear visco-elasticity 2.3. Non-linear viscoelasticity 3. Rheometry 4. Parameters affecting rheology 1. Rheological Phenomena: Do real melts behave according to Newton’s law? Deviation 1: Mayonnaise: resistance (viscosity) decreases with increasing shear rate: shear thinning Starch solution: resistance increases with increasing shear rate: shear thickening This is a non-linearity: η(γ&) Do real melts behave according to Newton’s law? Deviation 2: example silly putty t < τ t > τ The response of the material depends on the time scale: * Short times: elastic like behaviour * Long times: liquid-like behaviour VISCO-ELASTIC BEHAVIOUR G(t) or G(t,γ) Linear non-linear Do real melts behave according to Newton’s law? Deviation 3: Weissenberg effect Die Swell Normal stresses Do real melts behave according to Newton’s law? deviation 4: Ductless Syphon η(ext) > > η(shear) In summary: Newtonian behaviour real behaviour 1.